10x+20x(50-2x)=710

Solution for 10x+20x(50-2x)=710 equation:

Simplifying
10x + 20x(50 + -2x) = 710
10x + (50 * 20x + -2x * 20x) = 710
10x + (1000x + -40x2) = 710

Combine like terms: 10x + 1000x = 1010x
1010x + -40x2 = 710

Solving
1010x + -40x2 = 710

Solving for variable 'x'.

Reorder the terms:
-710 + 1010x + -40x2 = 710 + -710

Combine like terms: 710 + -710 = 0
-710 + 1010x + -40x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-71 + 101x + -4x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-71 + 101x + -4x2)' equal to zero and attempt to solve:

Simplifying
-71 + 101x + -4x2 = 0

Solving
-71 + 101x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
17.75 + -25.25x + x2 = 0

Move the constant term to the right:

Add '-17.75' to each side of the equation.
17.75 + -25.25x + -17.75 + x2 = 0 + -17.75

Reorder the terms:
17.75 + -17.75 + -25.25x + x2 = 0 + -17.75

Combine like terms: 17.75 + -17.75 = 0.00
0.00 + -25.25x + x2 = 0 + -17.75
-25.25x + x2 = 0 + -17.75

Combine like terms: 0 + -17.75 = -17.75
-25.25x + x2 = -17.75

The x term is -25.25x.  Take half its coefficient (-12.625).
Square it (159.390625) and add it to both sides.

Add '159.390625' to each side of the equation.
-25.25x + 159.390625 + x2 = -17.75 + 159.390625

Reorder the terms:
159.390625 + -25.25x + x2 = -17.75 + 159.390625

Combine like terms: -17.75 + 159.390625 = 141.640625
159.390625 + -25.25x + x2 = 141.640625

Factor a perfect square on the left side:
(x + -12.625)(x + -12.625) = 141.640625

Calculate the square root of the right side: 11.901286695

Break this problem into two subproblems by setting 
(x + -12.625) equal to 11.901286695 and -11.901286695.

Subproblem 1
x + -12.625 = 11.901286695

Simplifying
x + -12.625 = 11.901286695

Reorder the terms:
-12.625 + x = 11.901286695

Solving
-12.625 + x = 11.901286695

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '12.625' to each side of the equation.
-12.625 + 12.625 + x = 11.901286695 + 12.625

Combine like terms: -12.625 + 12.625 = 0.000
0.000 + x = 11.901286695 + 12.625
x = 11.901286695 + 12.625

Combine like terms: 11.901286695 + 12.625 = 24.526286695
x = 24.526286695

Simplifying
x = 24.526286695

Subproblem 2
x + -12.625 = -11.901286695

Simplifying
x + -12.625 = -11.901286695

Reorder the terms:
-12.625 + x = -11.901286695

Solving
-12.625 + x = -11.901286695

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '12.625' to each side of the equation.
-12.625 + 12.625 + x = -11.901286695 + 12.625

Combine like terms: -12.625 + 12.625 = 0.000
0.000 + x = -11.901286695 + 12.625
x = -11.901286695 + 12.625

Combine like terms: -11.901286695 + 12.625 = 0.723713305
x = 0.723713305

Simplifying
x = 0.723713305

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.526286695, 0.723713305}
Solution
x = {24.526286695, 0.723713305}